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A psychiatric patient shot when he ran at officers with a knife at a Sydney shopping centre was let down by police and the health system, his father says.

Jerry Sourian, 23, was shot several times at Westfield Hornsby after lunging at police with a large carving knife on Thursday.

His father, Jack Sourian, told the ABC his son's case had been mishandled by police and he should never have been allowed temporary leave from hospital.

It has been revealed Jerry Sourian — who was admitted to Hornsby Ku-ring-gai Hospital's psychiatric ward with schizophrenia seven weeks ago — was on an approved hour's leave with family on Wednesday when he ran away.

Three innocent women remain in hospital after they were hit with shrapnel when Mr Sourian was shot at in the busy shopping centre.

Elaine For, 65, Lorraine Pendleton, 82, Anne-Marie Petitfills, 60, received wounds to their lower limbs and abdomens in the chaos.

All three remain in a stable condition in hospital. Mr Sourian also remains in a stable condition in hospital under police guard.

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Police are now investigating whether a Taser or pepper spray could have been used instead of guns.

"A decision was made by those officers in a life-and-death situation," Assistant Commissioner Denis Clifford said yesterday.

The three women shot in the confrontation have reportedly been offered $30,000 each by the New South Wales Government under the Victims of Crime scheme.

Mr Sourian’s release came against recommendations from his doctor stipulating the man should not be released under any circumstance, and followed a consulting psychologist overruling the recommendation, the Sydney Morning Herald reports.

He had previously expressed homicidal tendencies towards police.

Mr Sourian had absconded from the facility while on day release last week and had flown to Melbourne.

He was brought back to the intensive care unit before being granted the hour's release during which he ran away.